You are the project manager for a medium$-$sized company planning to expand its office space to accommodate growing staff and improve facilities. The project involves several tasks requiring careful planning and coordination to be completed on time and within budget. Below is a list of the major tasks in this project, including their estimated durations and dependencies.

$\backslash$table$[[$Time Estimates $($week$)],[$Activity$,$Optimistic,Most Likely,Pessimistic,$\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[$A$,$Blueprint Drafting,$4,7,10,--],[$B$,$Permit Approval,$2,5,12,$A$],[$C$,$Material Procurement,$6,7,8,$A$],[$D$,$Foundation Work,$3,6,13,$B$],[$E$,$Structural Assembly,$6,8,9,$C$],[$F$,$Internal Wiring,$7,10,15,$D$,$E$]]$

Based on this information answer the following Questions:

a$)$ Calculate the expected activity times $($round to nearest integer$)$ and develop the activity network diagram $($AON$).$

b$)$ Calculate the activity slacks. What is the total project length? Make sure you fully label all nodes in the network.

c$)$ Identify the critical path. What are the alternative paths and how much slack time is associated with each noncritical path?

d$)$ Identify the burst activities and the merge activities.

e$)$ Given the activity variances, what is the likelihood of the project finishing on week $32?$ Suppose you wanted to have a $99\%$ confidence in the project finishing on time. How many How many additional weeks would your project team need to negotiate for to gain this $99\%$ likelihood?